The Investigation of 15-puzzle, Varikon Boxes, and Similar Variants
DOI:
https://doi.org/10.61173/2z34j345Keywords:
The Varikon box, 15-puzzle, permutational puzzles, permutation parityAbstract
The Varikon box, a 3-dimensional variant of the 15-puzzle, is the focus of this investigation. The goal is to investigate three questions: Whether swapping positions of two of its blocks affect its solvability, the number of distinct configurations of the puzzle, and the least number of steps needed for solving the 15-puzzle. First, we introduced our investigation with the same questions, yet for 15-puzzle, specifically using permutation parity to testify one’s solvability, then finding the pattern vice versa that is possible 15-puzzle configurations, and then all of it is mirrored onto the study of Varikon Boxes and other permutational puzzles.
References
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Dean&Francis Shingsui Eric Ren, Yuanyi He, Jiacheng He, Yuhao Cheng with_83_n3_Expected_Moves [Accessed 25 Aug. 2024] Contributors of Algorithms Insight. (2018) Implementing A-star(A*) to solve N-Puzzle [online] Available at: https:// algorithmsinsight.wordpress.com/graph-theory-2/a-star-ingeneral/implementing-a-star-to-solve-n-puzzle/ [Accessed 26 Aug. 2024] Achknowledgement We are deeply grateful to the support from Mr. Dan Ciubotaru, Mr. Xiangyin Chen, and Mr. Shanlin Guan for mathematical support and checking on our proves and calculations. We also thank GeoGebra.org as a tool for us to create multiple images for the demonstrations required in this paper.
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